Title: |
Multilevel Strategy for O-PCA-Based History Matching Using Mesh Adaptive Direct Search |
Author: |
Yimin Liu |
Year: |
2017 |
Degree: |
MS |
Adviser: |
Durlofsky |
File Size: |
2.1 MB |
View File: |
|
Access Count: |
473 |
Abstract:
Optimization-based principal component analysis (O-PCA) enables the low-dimensional representation of discrete (gridded) geological models while maintaining a reasonable level of geological realism. O-PCA has been successfully applied within a gradient-based history matching framework, with gradients provided using the adjoint procedure in Stanford`s Automatic-Differentiation-based General Purpose Research Simulator, AD-GPRS. However, the gradient of the mismatch function with respect to uncertain model parameters may not always be well defined or available, and this can limit the use of gradient-based history matching methods. Thus, in this study we explore the use of derivative-free optimization for O-PCA-based history matching.
We apply the mesh adaptive direct search (MADS) optimization algorithm in our history matching procedure. MADS is a pattern search method that parallelizes naturally and converges relatively quickly to a local minimum (when fully parallelized). In each MADS iteration, a local exploration of the objective function is performed by evaluating a set of trial points in the neighborhood of the current best point. The number of trial points is proportional to the number of optimization variables. Therefore, the dimension-reducing feature of O-PCA acts to significantly decrease the number of simulations required for history matching. To further reduce the computational cost, we develop a multilevel strategy that exploits the multiscale character of O-PCA. With this approach, the O-PCA coefficients are determined sequentially, at multiple levels. Coefficients associated with larger-scale features are history matched prior to those associated with smaller-scale features. Each MADS iteration thus requires the determination of fewer O-PCA coefficients than in the (standard) single-level strategy, and this leads to a reduction in the total number of simulations performed.
Results are presented for history matching a two-dimensional channelized reservoir model using MADS, with both the single-level and multilevel O-PCA-based approaches. The randomized maximum likelihood (RML) method is applied for uncertainty quantification; i.e., to provide multiple posterior (history matched) models. Both single-level and multilevel MADS strategies are shown to perform nearly as well as the gradient-based algorithm for this case. Although the gradient approach requires many fewer simulations, the multilevel strategies are shown to be comparable in terms of elapsed wall-clock time, assuming a sufficient number of processors is available. The derivative-free multilevel strategy is next applied for the simultaneous estimation of the O-PCA-based permeability field and for a set of parameters that define the (Corey-type) relative permeability curves. An RML procedure is again applied to provide multiple posterior models. Both single-level and multilevel MADS perform well for this case, and the multilevel strategy again significantly reduces the total number of simulations required. For this case a derivative-free capability is essential, as the adjoint method implemented in AD-GPRS does not currently provide gradients with respect to relative permeability parameters.
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